Capillary Surfaces in Manifolds with Nonnegative Scalar Curvature and Strictly Mean Convex Boundary

TL;DR

This paper investigates the geometric properties of manifolds with nonnegative scalar curvature and strictly mean convex boundary using stable capillary surfaces, providing obstructions and estimates relevant to their structure.

Contribution

It introduces new obstructions and estimates for manifolds with these curvature and boundary conditions using stable capillary surfaces.

Findings

Obstruction to filling 2-manifolds based on Urysohn width

Bandwidth estimate for such manifolds

New geometric properties established

Abstract

In this paper we use stable capillary surfaces (analogous to the $\mu$-bubble construction) to study manifolds with strictly mean convex boundary and nonnegative scalar curvature. We give an obstruction to filling 2-manifolds by such 3-manifolds based on the Urysohn width. We also obtain a bandwidth estimate and establish other geometric properties of such manifolds.